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Unformatted text preview: Molecular Dynamics Simulations 2011 Exercise 8: Suggested solutions Eero Holmstr om November 9, 2011 1. The standard deviation of the total energy per atom E (column 6 in the output of mdmorse ) for the set of 10 ps runs is presented in Table 1. The fluctuations are seen to be very small for cut-offs of 4.0, 6.0 and 8.0 A, but larger at 4.5 and 5.0 A. To explain this, lets look at Fig. 1, where the pair correlation function is plotted against the Morse potential. We see immediately that with r c = 4 . 5 and 5.0 A, we are at a peak in the pair correlation function, namely at the third and fourth nearest neighbors, respectively. Now, as the atoms vibrate due to thermal motion, the third neighbor in the first case and the fourth neighbor in the second case gets cut off one moment and taken into account again the next moment. This causes fluctuation in the potential energy and hence the total energy of the system. As the peak in the correlation function and the strength of the potential are smaller at...
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